On phantom thermodynamics with negative temperature

We discuss the thermodynamic properties of the Friedmann-Robertson-Walker universe with dark energy fluids labelled by $\omega=p/\rho<-1/3$. Using the integrability condition, we show that the phantom phase of $w<-1$ can still be thermodynamically allowed even when the temperature takes on negative values because in that case, there exists at least a condition of keeping physical values for $p$ and $\rho$